The Human Eye and the Colourful World - Detailed Notes

The Human Eye and the Colourful World ### Overview - This chapter explores the human eye, its functions, defects, and how we perceive color. It also discusses optical phenomena like rainbow formation, dispersion of white light, and atmospheric refraction. ### 10.1 The Human Eye - The human eye is a valuable and sensitive sense organ that enables us to see the world and colors around us. - It functions like a camera, forming an image on a light-sensitive screen called the retina. -

Cornea: Light enters the eye through the cornea, a thin membrane that forms a transparent bulge on the front surface of the eyeball. -
Eyeball: Approximately spherical, with a diameter of about $2.3$ cm. - Most refraction occurs at the cornea's outer surface. -
Crystalline Lens: Provides finer focal length adjustments to focus objects at varying distances onto the retina. -
Iris: A dark muscular diaphragm behind the cornea that controls the size of the pupil. -
Pupil: Regulates the amount of light entering the eye. - The eye lens forms an inverted real image on the retina. -
Retina: A delicate membrane with numerous light-sensitive cells. -
Light-sensitive cells: Activated by illumination, generating electrical signals sent to the brain via optic nerves. - The brain interprets these signals, processing information to allow us to perceive objects. #### 10.1.1 Power of Accommodation - The eye lens is composed of a fibrous, jelly-like material. -
Ciliary Muscles: Modify the curvature of the eye lens, thus changing its focal length. - Relaxed muscles make the lens thin, increasing focal length for clear distant vision. - Contracted muscles thicken the lens, decreasing focal length for clear near vision. -
Accommodation: The eye lens's ability to adjust its focal length. - The focal length cannot be decreased below a certain minimum limit. -
Least Distance of Distinct Vision (Near Point): About $25$ cm for a young adult with normal vision. This is the minimum distance at which objects can be seen distinctly without strain. -
Far Point: Infinity for a normal eye; the farthest point up to which the eye can see objects clearly. -
Cataract: A condition where the crystalline lens becomes milky and cloudy with old age, causing partial or complete vision loss. Cataract surgery can restore vision. ### 10.2 Defects of Vision and Their Correction - The eye may gradually lose its power of accommodation, leading to blurred vision due to refractive defects. - Three common refractive defects:- Myopia (Near-sightedness) - Hypermetropia (Far-sightedness) - Presbyopia - These defects can be corrected using suitable spherical lenses. #### (a) Myopia - Also known as near-sightedness. - Nearby objects are seen clearly, but distant objects are not. - The far point is nearer than infinity. - The image of a distant object is formed in front of the retina. - Causes:- Excessive curvature of the eye lens. - Elongation of the eyeball. - Corrected by using a concave lens of suitable power to bring the image back onto the retina. #### (b) Hypermetropia - Also known as far-sightedness. - Distant objects are seen clearly, but nearby objects are not. - The near point is farther away than the normal $25$ cm. - Light rays from a nearby object are focused at a point behind the retina. - Causes:- The focal length of the eye lens is too long. - The eyeball is too small. - Corrected by using a convex lens of appropriate power to provide additional focusing power for forming the image on the retina. #### (c) Presbyopia - The power of accommodation decreases with aging. - The near point recedes away, making it difficult to see nearby objects comfortably without corrective eyeglasses. - Causes:- Gradual weakening of the ciliary muscles. - Diminishing flexibility of the eye lens. - May require bi-focal lenses (both concave and convex lenses).- The upper portion has a concave lens for distant vision. - The lower part has a convex lens for near vision. - Can be corrected with contact lenses or surgical interventions. ### Eye Donation - Eyes can be donated after death to restore vision to blind individuals. - Corneal transplantation can cure corneal blindness. - Eye donors can be of any age group or sex and can include those who use spectacles or have had cataract surgery. - People with diabetes, hypertension, or asthma (without communicable diseases) can also donate. - Eyes must be removed within $4-6$ hours after death. - The identities of both the donor and the recipient remain confidential. - One pair of eyes can give vision to up to four corneal blind people. ### 10.3 Refraction of Light Through a Prism - Light refracted through a rectangular glass slab emerges parallel to the incident ray but is slightly displaced laterally. - A triangular glass prism has two triangular bases and three rectangular lateral surfaces, which are inclined to each other. - The angle between its two lateral faces is called the angle of the prism. - When light passes through a prism, it bends towards the normal when entering from air to glass and away from the normal when entering from glass to air. - The emergent ray bends at an angle to the direction of the incident ray. This angle is called the angle of deviation ( $\angle D$ ). ### 10.4 Dispersion of White Light by a Glass Prism - White light is split into its component colors when passed through a prism. - The sequence of colors is Violet, Indigo, Blue, Green, Yellow, Orange, and Red (VIBGYOR). - The band of colored components is called its spectrum. - The splitting of light into its component colors is called dispersion. - Different colors of light bend through different angles; violet bends the most, and red bends the least. - Isaac Newton discovered that sunlight is made up of seven colors by using two prisms: one to disperse the light and another to recombine it. - A rainbow is a natural spectrum caused by the dispersion of sunlight by tiny water droplets in the atmosphere. - Water droplets act like small prisms, refracting, dispersing, and internally reflecting sunlight. ### 10.5 Atmospheric Refraction - Atmospheric refraction is the refraction of light by the Earth’s atmosphere. - Hotter air is less dense and has a lower refractive index than cooler air, causing fluctuations in the apparent position of objects seen through it. -
Twinkling of Stars: Due to atmospheric refraction of starlight. The starlight bends towards the normal as it enters the Earth’s atmosphere. The apparent position of the star fluctuates, causing the star to twinkle. - Planets do not twinkle because they are closer and seen as extended sources; the variations in light average out. -
Advance Sunrise and Delayed Sunset: The Sun is visible about 2 minutes before actual sunrise and 2 minutes after actual sunset due to atmospheric refraction. ### 10.6 Scattering of Light - The interaction of light with objects gives rise to spectacular phenomena like the blue color of the sky and the reddening of the sun at sunrise and sunset. -
Tyndall Effect: The scattering of light by colloidal particles makes the path of a light beam visible. - The Earth’s atmosphere is a heterogeneous mixture of minute particles that scatter light. - The color of scattered light depends on the size of the scattering particles. Very fine particles scatter mainly blue light, while larger particles scatter longer wavelengths. -
Why is the Sky Blue?: Air molecules and fine particles scatter blue light more strongly than red light. - If the Earth had no atmosphere, the sky would appear dark. - Danger signal lights are red because red light is scattered the least by fog or smoke, making it visible over distances. ### Total Internal Reflection (TIR) - Total Internal Reflection occurs when light travels from a denser medium to a rarer medium at an angle of incidence greater than the critical angle. - Conditions for TIR:

Light must travel from a denser medium to a rarer medium.
The angle of incidence in the denser medium must be greater than the critical angle. - Applications of TIR:
Optical fibers: Used in communication and medical diagnostics.
-Prisms: Used in binoculars and periscopes. - Sparkling of diamond: Due to the high refractive index and small critical angle, light undergoes multiple total internal reflections. ### Critical Angle - The critical angle is the angle of incidence in a denser medium for which the angle of refraction in the rarer medium is $90$ degrees. - It is the maximum angle of incidence for which refraction can occur. - If the angle of incidence exceeds the critical angle, total internal reflection occurs. - The critical angle ( $\thetac$ ) can be calculated using Snell's Law: $\thetac = \sin^{-1}(\frac{n2}{n1})$ , where $n1$ is the refractive index of the denser medium and $n2$ is the refractive index of the rarer medium. ### Key Concepts -
Accommodation: The ability of the